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MATHEMATICS

JAMB 2007 - Question 39

Mathematics 2007 JAMB Past Questions - Question 39: Calculate the length of an arc of a circle of diameter 14cm,which subtends an angle of 90° at the center of the circle.

Calculate the length of an arc of a circle of diameter 14cm,which subtends an angle of 90° at the center of the circle.

A: 7 /2π cm

B: 7πcm

C: 14πcm

D: 7π/4 cm

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Correct Answer

Explanation

The length of an arc = Ñ³/360 X 2 πR (90/360 X 2/1 X π X 7) cm = 7 π/2cm To calculate the length of an arc of a circle, we need to know the radius (r) of the circle and the central angle (θ) subtended by the arc.Given that the diameter of the circle is 14 cm, we can find the radius by dividing the diameter by 2:r = 14 cm / 2 = 7 cmThe central angle is given as 90 degrees (90â�°).The formula to calculate the length of an arc is:Arc Length = (θ/360) * 2πrSubstituting the values into the formula:Arc Length = (90/360) * 2π * 7 cmSimplifying:Arc Length = (1/4) * 2π * 7 cmArc Length = (1/2)π * 7 cmArc Length = (7/2)π cmTherefore, the length of the arc is (7/2)π cm, which is approximately 10.99 cm.